EP1817547B1 - Method and device for navigating and positioning an object relative to a patient - Google Patents
Method and device for navigating and positioning an object relative to a patient Download PDFInfo
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- EP1817547B1 EP1817547B1 EP05813615A EP05813615A EP1817547B1 EP 1817547 B1 EP1817547 B1 EP 1817547B1 EP 05813615 A EP05813615 A EP 05813615A EP 05813615 A EP05813615 A EP 05813615A EP 1817547 B1 EP1817547 B1 EP 1817547B1
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B90/00—Instruments, implements or accessories specially adapted for surgery or diagnosis and not covered by any of the groups A61B1/00 - A61B50/00, e.g. for luxation treatment or for protecting wound edges
- A61B90/36—Image-producing devices or illumination devices not otherwise provided for
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
- A61B2034/2046—Tracking techniques
- A61B2034/2048—Tracking techniques using an accelerometer or inertia sensor
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
- A61B2034/2046—Tracking techniques
- A61B2034/2051—Electromagnetic tracking systems
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B90/00—Instruments, implements or accessories specially adapted for surgery or diagnosis and not covered by any of the groups A61B1/00 - A61B50/00, e.g. for luxation treatment or for protecting wound edges
- A61B90/39—Markers, e.g. radio-opaque or breast lesions markers
- A61B2090/3954—Markers, e.g. radio-opaque or breast lesions markers magnetic, e.g. NMR or MRI
- A61B2090/3958—Markers, e.g. radio-opaque or breast lesions markers magnetic, e.g. NMR or MRI emitting a signal
Definitions
- the invention relates to a method and apparatus for navigating and positioning an object relative to a patient during a medical operation in the operating room.
- the process of navigating and positioning may be the placement of a hip prosthesis in an exactly predicted position relative to the femur of the patient. So far, correct positioning has been visually checked by using cameras in the operating room. In this case, visually recognizable marks were applied to the object to be navigated or the device to be navigated. Also in the patient such marks were provided.
- the DE 4225112 describes an optical positioning. Although such a system operates with the required accuracy, it has numerous disadvantages. A system required for this with several cameras and a control unit is associated with very high costs in the range of several 10,000, - €.
- Such a system is based on reference, ie it is in principle only stationary use. If the system is to be used at a different location, the cameras required for this purpose must be rebuilt again at exactly predetermined locations. Furthermore, it proves to be disadvantageous that only a limited work area in the order of a dimension of about 1 m is available. Particularly disadvantageous is the problem of shading. The system can only work if the related brands can be captured simultaneously by all required cameras. If OP staff between such Brand and a camera or other operating equipment is positioned there, the system is not working.
- the present invention has for its object to improve a method and an apparatus of the type described above in such a way that the aforementioned disadvantages do not occur or are largely overcome.
- the object for example a prosthesis part or a surgical device
- the operating room staff can change the relevant object with regard to its position and orientation until it reaches the desired predetermined position relative to the patient or relative to a region of the patient.
- the claimed device is associated with much lower costs than the application of the optical detection technique described above.
- the system according to the invention is largely transportable; it requires with the exception of attachable to the object and the patient sensor devices no larger equipment that would have to be mounted consuming at exactly predetermined positions stationary.
- the three-dimensional inertial sensors having sensor devices are also largely miniaturized, they can be realized in volumes of a few millimeters dimension.
- the sensor devices can be fastened and released again at a predetermined location and in a predetermined orientation on the said object on the one hand and on an equally predetermined position on the patient on the other hand.
- the sensor devices advantageously have a preferably visually recognizable one Orientation on which allows a correct determination of the object or on the patient.
- the sensor devices have fastening means for detachably fixing the sensor device to the object and to the patient.
- This may be, for example, clamping or clip-like fastening means.
- the first and in particular also the second sensor device preferably have three acceleration sensors whose signals can be used to calculate a translatory movement, and additionally three rotation rate sensors whose measured values can be used to determine the orientation in space.
- magnetic field sensors can advantageously be provided for determining the orientation of the object in space.
- the magnetic field sensors detect components of the earth's magnetic field and are in turn able to provide information about the orientation of the sensor device in space.
- the computing means of the device according to the invention comprises means for the execution of a per se DE 103 12 154 A1 have known quaternion algorithm.
- the computing means have means for applying a previously determined and stored compensation matrix, which compensating matrix a deviation of the orientation of the axes of the three rotation rate sensors from an assumed orientation of the axes bill each other and by their application Compensated for the calculation of the rotation angle resulting error.
- the computing means have means for executing a Kalman filter algorithm.
- inertial sensors deliver measurements based on acceleration
- these measured values are integrated twice to determine position data in the case of acceleration sensors, and are easily integrated in the case of yaw rate sensors.
- errors are gradually added up by integration.
- the method and the device related thereto is designed so that before the start of a data take and then again, as soon as a resting of Device is detected for a certain period of time, an offset value of the output signal of the rotation rate sensors is determined and is subsequently deducted until the next determination of this offset value for the respective rotation rate sensors, so that it does not enter into the integration. In this way, it is ensured that a new current offset value is determined again and again, so that the greatest possible accuracy is achieved.
- the inverse diagonal elements of the non-orthogonality matrix in the equation would be 0 in an ideal system.
- the inaccuracies are due to manufacturing inaccuracies that cause the axes of the yaw rate sensors to be neither orthogonal to each other in a predetermined orientation to a housing of the sensor device.
- the accuracy of determining the orientation is also increased by applying a quaternion algorithm of the type defined below to the three angles of rotation for each measurement data acquisition and determination of the three angles of rotation in order to determine the current orientation of the object in space calculate.
- the Further improvement is due to the following circumstance: If one were to use the infinitesimal angle of rotation about a respective axis to determine the orientation change of the object obtained by simple integration at each infinitesimal step of the scan, ie, the measurement data taking such that the rotations are successively about the respective axis would be performed, this would result in a mistake.
- This error is due to the fact that the measurement data of the three sensors are taken at the same time, because a rotation usually takes place simultaneously around three axes and is determined.
- the vector ⁇ consists of the individual rotations around the coordinate axes.
- a rotation of a point or vector can now be calculated as follows. First, the coordinates of the point or the vector is converted into a quaternion by equation Eq.16 and then the multiplication by rotation quaternion is performed (Eq.18). The result quaternion contains the rotated vector in the same notation. Assuming that the magnitude of a quaternion equals one, the inverted quaternion can be replaced by the conjugate (Eq.19).
- q red 1
- the vector ⁇ is the normal vector to the plane in which a rotation of the angle 1 ⁇ 2 ⁇ is performed.
- the angle corresponds to the magnitude of the vector ⁇ . Please refer Fig.1 ,
- the concrete implementation of the quaternion algorithm is in FIG. 2 represented and takes place as follows: Overall the entire calculation using unit vectors. Starting from the start orientation, the start unit vectors E x , E y and E z are determined.
- Eq. 22 calculates the rotation matrix.
- R q 0 2 + q 1 2 - q 2 2 - q 3 2 2 ⁇ q 1 ⁇ q 2 - q 0 ⁇ q 3 2 ⁇ q 1 ⁇ q 3 - q 0 ⁇ q 2 2 ⁇ q 1 ⁇ q 2 - q 0 ⁇ q 3 q 1 2 + q 2 2 - q 3 2 2 ⁇ q 2 ⁇ q 3 - q 0 ⁇ q 1 2 ⁇ q 1 ⁇ q 3 - q 0 ⁇ q 1 2 ⁇ q 1 ⁇ q 3 - q 0 ⁇ q 2 2 ⁇ q 2 ⁇ q 3 - q 0 ⁇ q 1 0 2 - q 1 2 - q 2 2 + q 3 2
- the rotation matrix R which is a 3 ⁇ 3 matrix
- a rotation quaternion q red (k) can be obtained.
- the starting quaternion is calculated by a multiplication with the rotation quaternion.
- a rotation quaternion q red (k) to be used for this step is then calculated.
- the quaternion q akt (k-1) formed in the previous step is then multiplied by this rotation quaternion q red (k) according to Equation 13 to obtain the current quaternion of the present k-th step, namely q akt (k). From this current quaternion, the current orientation of the object can then be specified in any desired representation for the currently performed scanning step.
- Kalman filtering algorithm can be used to improve accuracy in determining or calculating Increase position data.
- the concept of Kalman filtering, in particular indirect Kalman filtering assumes the existence of support information. The difference of information, which is obtained from measured values of sensors, and this support information then serves as input to the Kalman filter.
- support information for determining the position is in any case fundamentally unavailable.
- Figures 3 . 4 and 5 schematically show the inventive concept of a redundant parallel system for Kalman filtering, wherein two sensors are arranged so that their sensitive sensor axes extend parallel to each other ( FIG. 4 ).
- FIG. 5 illustrates this schematically in a feed-forward configuration as a concrete realization of a general indirect Kalman filter.
- a 1st order Gauss Markov process generates the acceleration error using white noise.
- the model is based on the fact that the position error is determined from the acceleration error by double integration. This results in equations 23 and 25.
- Equation 30 The general stochastic state space description for the equivalent time-discrete system model is given by Equations 30 and 31, respectively.
- k ⁇ T ⁇ x k
- k ⁇ T ⁇ e s k
- Equations 32 and 33 apply to the required time-discrete measurement equation.
- y k C ⁇ x k + v k
- y k C ⁇ e s k e v k e a k + v k ,
- Equation 33 v (k) is a vectorial white noise process.
- the difference between the two sensor signals applies as input for the Kalman filter. This results in equations 34 to 36 for the measurement equation.
- y k e a ⁇ 2 k - e a ⁇ 1 k
- y k 0 0 - 1 ⁇ e s ⁇ 1 k e v ⁇ 1 k e a ⁇ 1 k + 0 0 e a ⁇ 2 k
- Equation 44 to 47 apply.
- y k a 2 k + e a ⁇ 2 k - a 1 k + e a ⁇ 1 k
- y k a a ⁇ 2 k - e a ⁇ 1 k
- P ⁇ k + 1
- the system used describes a three-dimensional translation in three orthogonal spatial axes. These translations are described by the path s, the velocity v and the acceleration a.
- an additional acceleration sensor also supplies acceleration information for each spatial direction.
- the basic algorithm of the structure is shown in Figure 5.
- the actual measurement signal comes from an acceleration sensor in the form of acceleration a for each spatial axis.
- the Kalman filter algorithm provides an estimated value for the deviation of the acceleration signal ea for the three spatial directions x, y and z.
- FIGS. 1, 2 and 4 to 6 have already been explained in advance.
- the object to be positioned is provided at a predetermined location with the first sensor device.
- the object is then brought to rest in the room and thus referenced with a stationary coordinate system, for example the operating table, that the angles and accelerations determined from the signals of the rotation rate sensors and acceleration sensors are initially set to zero.
- An offset value is then determined during an absolute quiescent period of the subject, which is set at each sample, i. H. at each data take, is considered. This is a drift vector whose components comprise the determined offset values of the sensors.
- the aforementioned compensation matrix is determined, which is a deviation of the axes of the rotation rate sensors of an assumed orientation to each other and to a housing of the sensor device corresponds to or compensate for this deviation exactly.
- the sensor signals are detected at successive times, for example with a sampling rate of 10 to 30 Hz, in particular of approximately 20 Hz, and converted into infinitesimal rotation angles or position data by simple or double integration.
- a sampling rate 10 to 30 Hz, in particular of approximately 20 Hz
- the compensation matrix for the non-orthogonality of the rotation rate sensors is taken into account in order to achieve an increased accuracy in determining the orientation.
- the orientation of the rotated coordinate system of the object to the reference coordinate system could now be determined by the Euler method by specifying three angles. Instead, it proves to be advantageous if a quaternion algorithm of the type described above is performed to determine the orientation. As a result, instead of three rotations to be executed one after the other, a single transformation can be assumed, which further increases the accuracy of the orientation of the object system obtained therefrom.
- the object can be determined by other sensors, such as a three-dimensional magnetic field sensor, at arbitrary times the magnetic field acting on the object, which is the geomagnetic field known at a location.
- a three-dimensional acceleration sensor for measuring the gravitational acceleration.
- the measurement signals of the magnetic field sensors and the acceleration sensors can be combined to form an electronic three-dimensional compass which can indicate with high accuracy the orientation of the object in space, if no disturbing effects are present, preferably if the measured values were taken during rest of the object.
- the resulting orientation of the object in space can be used as support information for that orientation which was obtained only by the signals of the three rotation rate sensors.
- the measurement signals of the magnetic field sensors and the acceleration sensors are examined to see whether they are affected by disturbances or not. If this is not the case, they are compared as support information to be taken into account in the execution of the method with the orientation information obtained from the three rotation rate sensors.
- a Kalman filter algorithm is advantageously used. This is an estimation algorithm in which the information about the orientation of the object determined from the previously mentioned three-dimensional compass is used as correct support information when compared with the information about the orientation obtained from the rotation rate sensors.
- the measurement values of the acceleration sensors can also be improved by using Kalman filtering, namely as a substitute for otherwise accessible support information
- a parallel thereto arranged redundant acceleration sensor is provided for each acceleration sensor.
- an estimated value for the error-related deviation of the acceleration measured value signal for the respective spatial direction can be determined.
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Abstract
Description
Die Erfindung betrifft ein Verfahren und eine Vorrichtung zum Navigieren und Positionieren eines Gegenstands relativ zu einem Patienten während einer medizinischen Operation im Operationssaal. Beispielsweise kann es sich bei dem Prozess des Navigierens und Positionierens um die Anordnung einer Hüftprothese in einer exakt vorausberechneten Position relativ zum Oberschenkelknochen des Patienten handeln. Bislang wurde eine korrekte Positionierung durch Verwendung von Kameras im Operationssaal optisch überprüft. Hierbei waren auf dem zu navigierenden Gegenstand oder dem zu navigierenden Gerät optisch erkennbare Marken aufgebracht. Auch bei dem Patienten waren solche Marken vorgesehen. Die
Der vorliegenden Erfindung liegt die Aufgabe zugrunde, ein Verfahren und eine Vorrichtung der eingangs beschriebenen Art dahingehend zu verbessern, dass die vorgenannten Nachteile nicht auftreten oder weitestgehend überwunden werden.The present invention has for its object to improve a method and an apparatus of the type described above in such a way that the aforementioned disadvantages do not occur or are largely overcome.
Diese Aufgabe wird durch ein Verfahren und eine Vorrichtung mit den Merkmalen der unabhängigen Ansprüche 1 und 3 gelöst.This object is achieved by a method and an apparatus having the features of
Durch Anwendung des erfindungsgemäßen Verfahrens und der erfindungsgemäßen Vorrichtung lässt sich der Gegenstand, etwa ein Prothesenteil oder ein chirurgisches Gerät, in einer zuvor bestimmten Position am Patienten positionieren, oder anders ausgedrückt vermag das OP-Personal den betreffenden Gegenstand so bezüglich seiner Lage und Orientierung zu verändern, bis er die erwünschte vorbestimmte Position relativ zum Patienten oder relativ zu einem Bereich des Patienten erreicht hat. Die beanspruchte Vorrichtung ist mit weitaus geringeren Kosten verbunden als die Anwendung der eingangs beschriebenen Technik der optischen Erfassung. Das erfindungsgemäße System ist weitestgehend transportabel; es erfordert mit Ausnahme der an dem Gegenstand und dem Patienten befestigbaren Sensoreinrichtungen keine größeren Gerätschaften, die aufwendig an exakt vorbestimmten Positionen stationär montiert werden müssten. Die eine dreidimensionale Inertialsensorik aufweisenden Sensoreinrichtungen sind auch weitgehend miniaturisierbar, sie lassen sich in Volumina von wenigen Millimetern Abmessung realisieren. Diese Sensoreinrichtungen sind an einer vorbestimmten Stelle und in einer vorgegebenen Orientierung an dem besagten Gegenstand einerseits und an einer ebenso vorbestimmten Position am Patienten andererseits befestigbar und wieder lösbar. Die Sensoreinrichtungen weisen hierfür vorteilhafterweise eine vorzugsweise visuell erkennbare Orientierungshilfe auf, die eine korrekte Festlegung an dem Gegenstand bzw. an dem Patienten gestattet.By applying the method according to the invention and the device according to the invention, the object, for example a prosthesis part or a surgical device, can be positioned in a predetermined position on the patient, or in other words, the operating room staff can change the relevant object with regard to its position and orientation until it reaches the desired predetermined position relative to the patient or relative to a region of the patient. The claimed device is associated with much lower costs than the application of the optical detection technique described above. The system according to the invention is largely transportable; it requires with the exception of attachable to the object and the patient sensor devices no larger equipment that would have to be mounted consuming at exactly predetermined positions stationary. The three-dimensional inertial sensors having sensor devices are also largely miniaturized, they can be realized in volumes of a few millimeters dimension. These sensor devices can be fastened and released again at a predetermined location and in a predetermined orientation on the said object on the one hand and on an equally predetermined position on the patient on the other hand. For this purpose, the sensor devices advantageously have a preferably visually recognizable one Orientation on which allows a correct determination of the object or on the patient.
Es erweist sich auch als vorteilhaft, wenn die Sensoreinrichtungen Befestigungsmittel aufweisen zum lösbaren Festlegen der Sensoreinrichtung an dem Gegenstand und an dem Patienten. Hierbei kann es sich beispielsweise um klemmende oder klipsartig ausgebildete Befestigungsmittel handeln.It also proves to be advantageous if the sensor devices have fastening means for detachably fixing the sensor device to the object and to the patient. This may be, for example, clamping or clip-like fastening means.
Um im Zuge der Durchführung des Verfahrens Positionsdaten aus den Messwerten der ersten Sensoreinrichtung und der zweiten Sensoreinrichtung miteinander vergleichen zu können, ist es lediglich erforderlich, dass zu Beginn der Positionierung eine Referenzierung der Sensoreinrichtungen durchgeführt wird, indem beide Sensoreinrichtungen an einem gemeinsamen Ort oder an zwei in vorbestimmter bekannter Orientierung zueinander liegenden Orten zur Ruhe gebracht werden. Hiervon ausgehend wird dann durch Verwendung der dreidimensionalen Sensorik eine Verlagerung der Sensoreinrichtungen ermittelt und weiterer Datenverarbeitung zugeführt.In order to be able to compare position data from the measured values of the first sensor device and the second sensor device in the course of the implementation of the method, it is only necessary that a referencing of the sensor devices is carried out at the beginning of the positioning by both sensor devices at a common location or at two be brought to rest in predetermined known orientation to each other places. On this basis, a displacement of the sensor devices is then determined by using the three-dimensional sensor system and fed to further data processing.
Die erste und insbesondere auch die zweite Sensoreinrichtung weisen bevorzugtermaßen drei Beschleunigungssensoren auf, deren Signale zur Berechnung einer translatorischen Bewegung verwendbar sind, und zusätzlich drei Drehratensensoren, deren Messwerte zum Bestimmen der Orientierung im Raum verwendbar sind.The first and in particular also the second sensor device preferably have three acceleration sensors whose signals can be used to calculate a translatory movement, and additionally three rotation rate sensors whose measured values can be used to determine the orientation in space.
Zusätzlich zu den Drehratensensoren können in vorteilhafter Weise Magnetfeldsensoren zur Ermittlung der Orientierung des Gegenstands im Raum vorgesehen sein. Die Magnetfeldsensoren erfassen dabei Komponenten des Erdmagnetfelds und vermögen ihrerseits Informationen über die Orientierung der Sensoreinrichtung im Raum zu geben.In addition to the rotation rate sensors, magnetic field sensors can advantageously be provided for determining the orientation of the object in space. The magnetic field sensors detect components of the earth's magnetic field and are in turn able to provide information about the orientation of the sensor device in space.
Solchenfalls erweist es sich als vorteilhaft, wenn Mittel zum Vergleichen der aus Messwerten der Magnetfeldsensoren ermittelten Orientierung im Raum mit der aus Messwerten der Drehratensensoren ermittelten Orientierung im Raum vorgesehen sind. Zusätzlich kann ein Beschleunigungssensor für die Messung der Erdbeschleunigung vorgesehen sein, welcher ebenfalls zur Ermittlung der Orientierung der betrachteten Sensoreinrichtung im Raum verwendet werden kann.In such a case, it proves to be advantageous if means for comparing the orientation determined from measured values of the magnetic field sensors in space with the orientation determined from measured values of the rotation rate sensors in space are provided. In addition, an acceleration sensor for measuring the gravitational acceleration can be provided, which can also be used to determine the orientation of the considered sensor device in space.
Es erweist sich des Weiteren als besonders vorteilhaft, wenn die Rechenmittel der erfindungsgemäßen Vorrichtung Mittel zur Ausführung eines an sich aus
Des Weiteren erweist es sich als vorteilhaft, wenn die Rechenmittel Mittel zur Anwendung einer vor Beginn der Positionierung ermittelten und gespeicherten Ausgleichsmatrix aufweisen, welche Ausgleichsmatrix einer Abweichung der Orientierung der Achsen der drei Drehratensensoren von einer angenommenen Orientierung der Achsen zueinander Rechnung trägt und durch ihre Anwendung einen bei der Berechnung der Drehwinkel resultierenden Fehler kompensiert.Furthermore, it proves to be advantageous if the computing means have means for applying a previously determined and stored compensation matrix, which compensating matrix a deviation of the orientation of the axes of the three rotation rate sensors from an assumed orientation of the axes bill each other and by their application Compensated for the calculation of the rotation angle resulting error.
Ferner erweist es sich als vorteilhaft, wenn die Rechenmittel Mittel zur Ausführung eines Kalman-Filter-Algorithmus aufweisen.Furthermore, it proves to be advantageous if the computing means have means for executing a Kalman filter algorithm.
Da Inertialsensoren auf Beschleunigungsvorgänge zurückgehende Messwerte liefern, werden diese Messwerte zur Bestimmung von Positionsdaten im Falle von Beschleunigungssensoren zweifach integriert und im Falle von Drehratensensoren einfach integriert. Im Zuge dieser Integrationsvorgänge werden Fehler nach und nach durch Integration aufaddiert. Insofern erweist es sich als vorteilhaft, dass das Verfahren und die hierfür verwandte Vorrichtung so ausgebildet ist, dass vor Beginn einer Datennahme und dann immer wieder, sobald ein Ruhen der Vorrichtung für eine bestimmte Zeitdauer festgestellt wird, ein Offset-Wert des Ausgangssignals der Drehratensensoren ermittelt wird und nachfolgend bis zur nächstfolgenden Ermittlung dieser Offset-Wert für die jeweiligen Drehratensensoren in Abzug gebracht wird, so dass er nicht in die Integration eingeht. Auf diese Weise wird sichergestellt, dass immer wieder ein neuer aktueller Offset-Wert ermittelt wird, so dass größtmögliche Genauigkeit erreicht wird.Since inertial sensors deliver measurements based on acceleration, these measured values are integrated twice to determine position data in the case of acceleration sensors, and are easily integrated in the case of yaw rate sensors. In the course of these integration processes, errors are gradually added up by integration. In this respect, it proves to be advantageous that the method and the device related thereto is designed so that before the start of a data take and then again, as soon as a resting of Device is detected for a certain period of time, an offset value of the output signal of the rotation rate sensors is determined and is subsequently deducted until the next determination of this offset value for the respective rotation rate sensors, so that it does not enter into the integration. In this way, it is ensured that a new current offset value is determined again and again, so that the greatest possible accuracy is achieved.
Es wurde auch festgestellt, dass die konstruktionsbedingt nicht zu vermeidende Abweichung der Orientierung der Achsen der drei Drehratensensoren von einer angenommenen Orientierung sehr rasch bei der Berechnung der Drehwinkel zu Ungenauigkeiten führt. Dadurch, dass dieser Fehler durch Anwendung der für die betreffende Sensoreinrichtung zu bestimmenden Ausgleichsmatrix kompensiert wird, lässt sich eine den Anforderungen genügende Steigerung der Genauigkeit erreichen. Zur Ermittlung der Ausgleichsmatrix wird vor Beginn der Objektverfolgung eine hierfür verwandte Sensoreinrichtung in eine rotierende Bewegung um eine jeweilige Achse gebracht, und zwar unter Stillsetzung der beiden anderen Achsen. Anhand der hierbei erhaltenen Drehratensensorsignale wird die Ausgleichsmatrix errechnet und in einem Speicher der beanspruchten Vorrichtung hinterlegt. Für den rotatorischen Antrieb der Sensorvorrichtung kann ein Industrieroboter verwendet werden. Auf diese Weise kann die 3x3-Nichtorthogonalitätsmatrix durch Drehung um die einzelnen Raumachsen nacheinander aufgenommen werden.
Die Nebendiagonalelemente der Nichtorthogonalitätsmatrix in Gleichung wären bei einem idealen System 0. Die Ungenauigkeiten beruhen auf Fertigungsungenauigkeiten, die dazu führen, dass die Achsen der Drehratensensoren weder in einer vorbestimmten Orientierung zu einem Gehäuse der Sensoreinrichtung noch exakt orthogonal zueinander angeordnet sind.The inverse diagonal elements of the non-orthogonality matrix in the equation would be 0 in an ideal system. The inaccuracies are due to manufacturing inaccuracies that cause the axes of the yaw rate sensors to be neither orthogonal to each other in a predetermined orientation to a housing of the sensor device.
Wenn vorausgehend davon die Rede war, dass ein Offset-Wert bestimmt wird, wenn ein Ruhen der Vorrichtung für eine bestimmte Zeitdauer festgestellt wird, so wird hierunter die Bestimmung eines Driftvektors verstanden, und zwar für drei vorzugsweise orthogonal zueinander orientierte Drehratensensoren und für drei vorzugsweise orthogonal zueinander orientierte Beschleunigungssensoren. Auf diese Weise kann eine Matrix D ermittelt werden, deren Zeilen die Offsets der einzelnen Sensoren sind. Sie werden vorzugsweise zu Beginn einer Objektverfolgung und dann immer wieder bei einer detektierten Ruhelage neu ermittelt und für die weitere Datenverarbeitung zugrunde gelegt.
Die Genauigkeit der Bestimmung der Orientierung wird nach einer Ausführungsform der Erfindung auch dadurch erhöht, dass bei jeder Messdatennahme und Ermittlung der drei Drehwinkel ein Quaternionen-Algorithmus der nachfolgend definierten Art auf die drei Drehwinkel angewandt wird, um hieraus die aktuelle Orientierung des Objekts im Raum zu errechnen. Die hierdurch erzielte weitere Verbesserung beruht auf folgendem Umstand: Wenn man die durch einfache Integration bei jedem infinitesimalen Schritt der Abtastung, d. h. der Messdatennahme erhaltbaren infinitesimalen Drehwinkel um eine jeweilige Achse zur Bestimmung der Orientierungsänderung des Objekts so heranziehen würde, dass die Drehungen nacheinander um die jeweilige Achse durchgeführt würden, so würde hieraus ein Fehler resultieren. Dieser Fehler liegt darin begründet, dass die Messdaten der drei Sensoren zum gleichen Zeitpunkt genommen werden, weil eine Drehung in der Regel gleichzeitig um drei Achsen stattfindet und ermittelt wird. Wenn dann zur Ermittlung der Positionsveränderung die drei bestimmten Drehwinkel aber nacheinander als Drehungen um die jeweiligen Achsen berücksichtigt würden, so würde bei der Drehung um die zweite und die dritte Achse ein Fehler resultieren, da diese Achsen bereits im Zuge der ersten Drehung fehlerbehaftet in eine andere Orientierung gebracht wurden. Dem wird durch Anwendung des Quaternionen-Algorithmus auf die drei Drehwinkel begegnet. Auf diese Weise werden die drei Drehungen durch eine einzige Transformation ersetzt. Der Quaternionen-Algorithmus ist folgendermaßen definiert:According to an embodiment of the invention, the accuracy of determining the orientation is also increased by applying a quaternion algorithm of the type defined below to the three angles of rotation for each measurement data acquisition and determination of the three angles of rotation in order to determine the current orientation of the object in space calculate. The Further improvement is due to the following circumstance: If one were to use the infinitesimal angle of rotation about a respective axis to determine the orientation change of the object obtained by simple integration at each infinitesimal step of the scan, ie, the measurement data taking such that the rotations are successively about the respective axis would be performed, this would result in a mistake. This error is due to the fact that the measurement data of the three sensors are taken at the same time, because a rotation usually takes place simultaneously around three axes and is determined. If, however, the three specific angles of rotation were subsequently taken into account as rotations about the respective axes in order to determine the change in position, an error would result in the rotation about the second and the third axis since these axes already have errors in another during the first rotation Orientation were brought. This is countered by applying the quaternion algorithm to the three rotation angles. In this way, the three rotations are replaced by a single transformation. The quaternion algorithm is defined as follows:
Die Quaternion ist in Gl.1. definiert:
Durch Zusammenfassen der komplexen Anteile zu einem Vektor v und mit q0=w gelangt man zu der Schreibweise in Gl.9.
mit den Bedingungen Gl.10. und Gl.11.
with the conditions Eq. and Gl.11.
Für die Benutzung der Quaternionen gelten die Definitionen Gl. 12 bis Gl.17.
Konjugierte Quaternion
Conjugated quaternion
Betrag
Inversion
Multiplikation
Darstellung eines Vektors
Darstellung eines Skalars
Besondere Bedeutung für die inertiale Objektverfolgung erhält die Multiplikation. Diese stellt eine Rotation einer Quaternion dar. Dafür wird eine Rotationsquaternion Gl.18. eingeführt.
Der Vektor φ besteht aus den einzelnen Drehungen um die Koordinatenachsen.The vector φ consists of the individual rotations around the coordinate axes.
Eine Drehung eines Punkts oder Vektors kann nun wie folgt errechnet werden. Zunächst müssen die Koordinaten des Punkts oder der Vektor mittels Gleichung Gl.16 in eine Quaternion umgewandelt und anschließend die Multiplikation mit der Rotationsquaternion durchgeführt werden (Gl.18). Die Ergebnisquaternion enthält den rotierten Vektor in der gleichen Schreibweise. Unter der Voraussetzung, dass der Betrag einer Quaternion gleich eins ist, kann die invertierte Quaternion durch die konjugierte ersetzt werden (Gl.19).
wegen Gl. 20.
because of Eq. 20th
Wie kann man diese Operation verdeutlichen? Der vektor φ ist der Normalenvektor zu der Ebene, in der eine Drehung um den Winkel ½φ ausgeführt wird. Der Winkel entspricht dem Betrag des Vektors φ. Siehe
Aus
Die konkrete Umsetzung des Quaternionen Algorithmus ist in
Aus den Einheitsvektoren wird mit Hilfe von Gleichung Gl. 22 die Rotationsmatrix berechnet.
Ausgehend von einer Startorientierung des mit dem Objekt verbundenen Koordinatensystems, insbesondere ausgehend von sogenannten Einheitsstartvektoren, wird gemäß Gleichung 22 die Rotationsmatrix R, bei der es sich um eine 3x3-Matrix handelt, errechnet. Aus einer Umkehrung dieser Gleichung 22 lässt sich ein Rotationsquaternion qrot(k) erhalten. Mit Hilfe des Nullquaternions, welches sich aus den Nulleinheitsvektoren ergibt, wird durch eine Multiplikation mit dem Rotationsquaternion das Startquarternion berechnet. Bei der nächstfolgenden Abtastung, also bei der nächsten Messdatennahme und Integration zu aktuellen infinitesimalen Drehwinkeln A, B, C errechnet sich dann ein für diesen Schritt zu benutzendes Rotationsquaternion qrot(k). Das im vorherigen Schritt gebildete Quaternion qakt(k-1) wird dann mit diesem Rotationsquaternion qrot(k) gemäß Gleichung 13 multipliziert, um das aktuelle Quaternion des vorliegenden k-ten Schritts, nämlich qakt(k) zu erhalten. Aus diesem aktuellen Quaternion kann dann für den gerade durchgeführten Abtastschritt die aktuelle Orientierung des Objekts in beliebiger Darstellung angegeben werden.Starting from a start orientation of the coordinate system connected to the object, in particular starting from so-called unit start vectors, according to
Es wurde vorausgehend schon darauf hingewiesen, dass ein Kalman-Filteralgorithmus angewandt werden kann, um die Genauigkeit bei der Ermittlung oder Errechnung von Positionsdaten zu erhöhen. Das Konzept einer Kalman-Filterung, insbesondere einer indirekten Kalman-Filterung, geht von der Existenz einer Stützinformation aus. Die Differenz von Informationen, die aus Messwerten von Sensoren gewonnen werden, und dieser Stützinformation dient dann als Eingangssignal des Kalman-Filters. Da das erfindungsgemäße Verfahren und die Vorrichtung aber keine kontinuierliche Information von einem Referenzsystem erhalten, steht eine Stützinformation für die Positionsbestimmung jedenfalls grundsätzlich nicht zur Verfügung. Um dennoch die Anwendung indirekter Kalman-Filterung zu ermöglichen, wird vorgeschlagen, einen zweiten, parallel angeordneten Beschleunigungssensor zu verwenden. Die Differenz der Sensorsignale der parallelen Beschleunigungssensoren dient dann als Eingangssignal für das Kalman-Filter.
In vorteilhafter Weise werden beide Integrationsschritte in die Modellierung aufgenommen. Man erhält also einen Schätzfehler für den durch zweifache Integration zwangsläufig sich ergebenden Positionsfehler.
In diesem Konzept erzeugt ein Gauss-Markov-Prozess 1. Ordnung den Beschleunigungsfehler mit Hilfe von weißem Rauschen. Das Modell beruht darauf, dass aus dem Beschleunigungsfehler durch zweifache Integration der Positionsfehler ermittelt wird. Es ergeben sich die Gleichungen 23 und 25.
In Anlehnung an die allgemeine stochastische Zustandsraumbeschreibung eines zeitkontinuierlichen Systemmodells mit Zustandsvektor x(t), Zustandsübergangsmatrix Φ(T), stochastischer Streumatrix G und Messrauschen w(t) ergibt sich die Systemgleichung 26 bzw. 27.
Für das Messrauschen w(t) gelten die Gleichungen 28 und 29.
Die allgemeine stochastische Zustandsraumbeschreibung für das äquivalente zeitdiskrete Systemmodell ergibt sich nach Gleichung 30 bzw. 31.
Für die erforderliche zeitdiskrete Messgleichung gelten die Gleichungen 32 und 33.
In Gleichung 33 ist v(k) ein vektorieller weißer Rauschprozess. Als Eingang für das Kalman-Filter gilt die Differenz der beiden Sensorsignale. Damit ergeben sich für die Messgleichung die Gleichungen 34 bis 36.
In diesem Modell sollte sowohl e a1(k) als auch e a2(k) als Gauss-Markov-Prozess erster Ordnung modelliert werden. Dazu dient der Ansatz nach Gleichung 37.
Der äquivalente zeitdiskrete Ansatz dazu folgt nach Gleichung 38.
Betrachtet man ea2(k) als weiteren Zustand ergibt sich das erweiterte Systemmodell nach Gleichung 39 und 40.
Dabei gelten die Gleichungen 41 bis 43.
Für das erweiterte Messmodell gelten die Gleichungen 44 bis 47.
Bei dieser Messgleichung handelt es sich um eine perfekte und damit fehlerfreie Messung, d.h. es tritt kein Messrauschen v(k) auf. Damit bedarf es einer Modellierung nach Gleichung 48.
Die Kovarianzmatrix R des Messrauschens ist damit singulär, d.h. R-1 existiert nicht. Die Existenz von R-1 ist hinreichende aber nicht notwendige Bedingung für die Stabilität bzw. für die stochastische Beobachtbarkeit des Kalman-Filters. Es gibt nun zwei Möglichkeiten auf den Umstand der Singularität zu reagieren:
- 1. Verwendung von R=0. Das Filter kann stabil sein. Da hier ohnehin nur der Bedarf für kurzzeitige Stabilität besteht, kann auf Langzeitstabilität verzichtet werden.
- 2. Verwendung eines reduzierten Beobachters.
- 1. Use of R = 0. The filter can be stable. Since there is only a need for short-term stability anyway, long-term stability can be dispensed with.
- 2. Use of a reduced observer.
In diesem Konzept wird die varianz R=0 verwendet. Damit arbeiten die verwendeten Filter hinreichend stabil.In this concept the varianz R = 0 is used. Thus, the filters used sufficiently stable.
Die Kalman-Filter-Gleichungen für das eindimensionale System in diskreter Form ergeben sich zu Gleichungen 49 bis 50.The Kalman filter equations for the one-dimensional system in discrete form result in equations 49-50.
Bestimmung der Kalmanverstärkung nach Gleichung 49.
Aktualisierung der Zustandsvorhersage nach Gleichung 50.
Wobei Gleichung 51 gilt.
Aktualisierung der Kovarianzmatrix des Schätzfehlers nach Gleichung 52 bzw. 53.
Ermittlung des Prädiktionswertes des Systemzustandes nach Gleichung 54.
Ermittlung des Prädiktionswertes der Kovarianzmatrix des Schätzfehlers nach Gleichung 55.
Damit ist der Filterzyklus komplett durchlaufen und beginnt für den nächsten Messwert erneut. Das Filter arbeitet rekursiv, wobei die Schritte der Vorhersage und der Korrektur bei jeder Messung durchlaufen werden.This completes the filter cycle and begins again for the next measured value. The filter works recursively, with the steps of prediction and correction going through each measurement.
Das verwendete System beschreibt eine dreidimensionale Translation in drei orthogonalen Raumachsen. Diese Translationen werden durch den Weg s, die Geschwindigkeit v und die Beschleunigung a beschrieben. Für ein indirektes Kalman-Filter liefert jeweils ein zusätzlicher Beschleunigungssensor für jede Raumrichtung ebenfalls eine Beschleunigungsinformation.The system used describes a three-dimensional translation in three orthogonal spatial axes. These translations are described by the path s, the velocity v and the acceleration a. For an indirect Kalman filter, an additional acceleration sensor also supplies acceleration information for each spatial direction.
Der grundsätzliche Algorithmus des Aufbaus wird in Bild 5 dargestellt. Das eigentliche Messsignal kommt für jede Raumachse von einem Beschleunigungssensor in Form der Beschleunigung a. Mit Hilfe der Zusatzinformation in Form des Sensorsignals des zweiten Beschleunigungssensors für jede Raumachse liefert der Kalman-Filter-Algorithmus einen Schätzwert für die Abweichung des Beschleunigungssignals ea für die drei Raumrichtungen x, y und z.The basic algorithm of the structure is shown in Figure 5. The actual measurement signal comes from an acceleration sensor in the form of acceleration a for each spatial axis. With the aid of the additional information in the form of the sensor signal of the second acceleration sensor for each spatial axis, the Kalman filter algorithm provides an estimated value for the deviation of the acceleration signal ea for the three spatial directions x, y and z.
Weitere Merkmale, Einzelheiten und Vorteile der Erfindung ergeben sich aus den Patentansprüchen und aus der zeichnerischen Darstellung und nachfolgenden Beschreibung der Erfindung. In der Zeichnung zeigt:
- Figur 1
- die Darstellung der Rotation eines Vektors mittels Quaternionen;
Figur 2- ein Flussdiagramm, welches die Anwendung des Quaternionen-Algorithmus verdeutlicht;
Figur 3- ein Flussdiagramm, welches die Durchführung des erfindungsgemäßen Verfahrens verdeutlicht;
Figur 4- die schematische Darstellung eines Beschleunigungssensors und eines parallel hierzu angeordneten redundanten Beschleunigungssensors;
- Figur 5
- die schematische Andeutung eines Kalman-Filters mit INS-Fehlermodellierung in Feed-Forward-Konfiguration;
- Figur 6
- eine schematische Darstellung des Ergebnisses der Anwendung einer Kalman-Filterung.
- FIG. 1
- the representation of the rotation of a vector by means of quaternions;
- FIG. 2
- a flow chart illustrating the application of the quaternion algorithm;
- FIG. 3
- a flow chart illustrating the implementation of the method according to the invention;
- FIG. 4
- the schematic representation of an acceleration sensor and a parallel thereto arranged redundant acceleration sensor;
- FIG. 5
- the schematic hint of a Kalman filter with INS error modeling in feed-forward configuration;
- FIG. 6
- a schematic representation of the result of the application of a Kalman filtering.
Die
Wie bereits erwähnt, wird zu Beginn der Objektverfolgung der zu positionierende Gegenstand an vorbestimmter Stelle mit der ersten Sensoreinrichtung versehen. Der Gegenstand wird dann im Raum zur Ruhe gebracht und derart mit einem ortsfesten Koordinatensystem, beispielsweise der OP-Tisch, referenziert, dass die aus den Signalen der Drehratensensoren und Beschleunigungssensoren ermittelten Winkel und Beschleunigungen zunächst zu 0 gesetzt werden. Es wird dann während einer absoluten Ruhephase des Gegenstands ein Offset-Wert ermittelt, der bei jeder Abtastung, d. h. bei jeder Datennahme, berücksichtigt wird. Es handelt sich hierbei um einen Driftvektor, dessen Komponenten die ermittelten Offset-Werte der Sensoren umfassen.As already mentioned, at the beginning of the object tracking, the object to be positioned is provided at a predetermined location with the first sensor device. The object is then brought to rest in the room and thus referenced with a stationary coordinate system, for example the operating table, that the angles and accelerations determined from the signals of the rotation rate sensors and acceleration sensors are initially set to zero. An offset value is then determined during an absolute quiescent period of the subject, which is set at each sample, i. H. at each data take, is considered. This is a drift vector whose components comprise the determined offset values of the sensors.
Als ganz besonders vorteilhaft erweist es sich, dass jedes Mal, wenn ein Ruhen der Sensoreinrichtung detektiert und zu Grunde gelegt wird, die Offset-Werte der Sensoren von neuem ermittelt und der weiteren Berechnung der Position und Orientierung zugrundegelegt werden.It proves to be particularly advantageous that each time a resting of the sensor device is detected and taken as a basis, the offset values of the sensors are determined anew and the further calculation of the position and orientation is taken as the basis.
Ferner wird die zuvor erwähnte Ausgleichsmatrix ermittelt, die einer Abweichung der Achsen der Drehratensensoren von einer angenommenen Orientierung zueinander und zu einem Gehäuse der Sensoreinrichtung entspricht bzw. diese Abweichung genau ausgleichen soll.Furthermore, the aforementioned compensation matrix is determined, which is a deviation of the axes of the rotation rate sensors of an assumed orientation to each other and to a housing of the sensor device corresponds to or compensate for this deviation exactly.
Die vorstehenden Ausführungen gelten für die zweite Sensoreinrichtung, die am Patienten festgelegt werden soll, entsprechend.The above explanations apply correspondingly to the second sensor device which is to be fixed on the patient.
Bei der Durchführung des Positionierens und Orientierens werden zu aufeinander folgenden Zeitpunkten, etwa mit einer Abtastrate von 10 bis 30 Hz, insbesondere von ca. 20 Hz, die Sensorsignale erfasst und durch einfache oder zweifache Integration in infinitesimale Drehwinkel bzw. in Positionsdaten umgerechnet. Dabei wird aber die Ausgleichsmatrix für die Nichtorthogonalität der Drehratensensoren berücksichtigt, um zu einer erhöhten Genauigkeit bei der Ermittlung der Orientierung zu gelangen.When carrying out the positioning and orientation, the sensor signals are detected at successive times, for example with a sampling rate of 10 to 30 Hz, in particular of approximately 20 Hz, and converted into infinitesimal rotation angles or position data by simple or double integration. However, the compensation matrix for the non-orthogonality of the rotation rate sensors is taken into account in order to achieve an increased accuracy in determining the orientation.
Anhand der infinitesimal kleinen Winkeländerungen, die jeweils aus den Messsignalen der drei Drehratensensoren ermittelt wurden, könnte nun nach dem Eulerschen Verfahren durch Angabe von drei Winkeln die Orientierung des verdrehten Koordinatensystems des Objekts zum Referenzkoordinatensystem ermittelt werden. Stattdessen erweist es sich als vorteilhaft, wenn zur Ermittlung der Orientierung ein Quaternionen-Algorithmus der eingangs beschriebenen Art durchgeführt wird. Hierdurch kann anstelle von drei nacheinander auszuführenden Drehungen eine einzige Transformation angenommen werden, was die Genauigkeit der hieraus gewonnenen Orientierung des Objektsystems weiter erhöht.Based on the infinitesimally small angle changes, which were determined in each case from the measurement signals of the three rotation rate sensors, the orientation of the rotated coordinate system of the object to the reference coordinate system could now be determined by the Euler method by specifying three angles. Instead, it proves to be advantageous if a quaternion algorithm of the type described above is performed to determine the orientation. As a result, instead of three rotations to be executed one after the other, a single transformation can be assumed, which further increases the accuracy of the orientation of the object system obtained therefrom.
Im Ergebnis der Durchführung des Quaternionen-Algorithmus ist die Orientierung des Objekts im Raum gegeben.As a result of performing the quaternion algorithm, the orientation of the object in space is given.
Wie in
Wie vorausgehend im Einzelnen beschrieben wurde, können auch die Messwerte der Beschleunigungssensoren durch Anwendung einer Kalman-Filterung verbessert werden, indem nämlich als Ersatz für eine anderweitig zugängliche Stützinformation vorzugsweise für jeden Beschleunigungssensor ein parallel hierzu angeordneter redundanter Beschleunigungssensor vorgesehen wird. Mit Hilfe dieser Zusatzinformation in Form des Messwertsignals des zweiten Beschleunigungssensors für jede Raumachse kann ein Schätzwert für die fehlerbedingte Abweichung des Beschleunigungsmesswertsignals für die jeweilige Raumrichtung ermittelt werden.As previously described in detail, the measurement values of the acceleration sensors can also be improved by using Kalman filtering, namely as a substitute for otherwise accessible support information Preferably, a parallel thereto arranged redundant acceleration sensor is provided for each acceleration sensor. With the aid of this additional information in the form of the measured value signal of the second acceleration sensor for each spatial axis, an estimated value for the error-related deviation of the acceleration measured value signal for the respective spatial direction can be determined.
Claims (14)
- Method for navigating and positioning an object relative to a patient during surgery in an operating theatre, characterized in that the position and orientation in the room space of both the object and the patient or of a relevant area of the patient relative to a referencing framework is determined quasi continuously according to a sensing rate by means of three-dimensional inertial sensors, and that from this the current position and orientation of the object relative to the patient is determined, that this position and orientation are compared with a desired, predetermined position and orientation, and that there is an indication as to how the position of the object should be modified in order to be placed in the desired predetermined position and orientation.
- Method according to Claim 1, characterized in that the sensing rate is 10 - 50 Hz, especially 10 - 40 Hz, especially 10 - 30 Hz and further especially 15 - 25 Hz.
- Apparatus for the implementation of the method according to Claim 1 or 2 comprising a first sensor device with acceleration sensors and rotational rate sensors that is attachable to and again removable from a first predetermined area of the object, and a second sensor device with acceleration sensors and rotational rate sensors that is attachable to and again removable from a patient, a memory, where the desired predetermined position and orientation of the object relative to the patient is stored, and computing means to determine the position and orientation from the measured sensor values, and computing means to compare the determined position and orientation with the predetermined position and orientation, and indication means to indicate how the position of the object should be modified in order to be placed into the desired predetermined position and orientation.
- Apparatus according to Claim 3, characterized in that the measured values of the sensor device can be acquired and processed at a sensing rate of 10 - 50 Hz, especially 10 - 40 Hz, especially 10 - 30 Hz and further especially 15 - 25 Hz.
- Apparatus according to Claim 3 or 4, characterized in that the sensor devices have an orientation aid, which allows correct fastening to the object and to the patient, respectively.
- Apparatus according to Claim 3, 4 or 5, characterized in that the sensor devices have means of fastening for the removable attachment of the sensor device to the object and the patient.
- Apparatus according to one or more of Claims 3 - 6, characterized in that the first and, especially also the second sensor device comprise three acceleration sensors, whose signals may be used for the calculation of translational movements, and in addition three rotational rate sensors, whose measured values may be used for the determination of the orientation in the room.
- Apparatus according to one or more of Claims 3 - 7, characterized in that the computing means comprise means for the execution of a quaternion algorithm.
- Apparatus according to one or more of Claims 3 - 8, characterized in that the computing means comprise means for the application of a compensation matrix that is determined and stored prior to the start of positioning, said compensation matrix allowing for a deviation of the axial orientation of the three rotational rate sensors from an assumed orientation of the axes toward each other and compensating for errors resulting from the calculation of the rotation angles.
- Apparatus according to one or more of Claims 3 - 9, characterized in that the computing means have means for executing a Kalman filter algorithm.
- Apparatus according to one or more of claims 3 - 10, characterized in that in addition to the rotational rate sensors, magnetic field sensors for the determination of the space orientation of the object are provided.
- Apparatus according to Claim 11, characterized in that means for comparing the space orientation determined from the values measured by the magnetic field sensors with the space orientation determined by the values measured by the rotational rate sensors are provided.
- Apparatus according to Claim 11 or 12, characterized in that means for comparing the space orientation determined from the values measured by the magnetic field sensors with the space orientation determined by the values measured by a gravitational acceleration sensor are provided.
- Apparatus according to one or more of Claims 3 - 13, characterized in that for each acceleration sensor a redundant acceleration sensor arranged parallel to it is provided for the implementation of Kalman filtering.
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-
2005
- 2005-11-22 EP EP05813615A patent/EP1817547B1/en not_active Not-in-force
- 2005-11-22 AT AT05813615T patent/ATE554366T1/en active
- 2005-11-22 WO PCT/EP2005/012473 patent/WO2006058633A1/en active Application Filing
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2007
- 2007-06-01 US US11/809,682 patent/US20070287911A1/en not_active Abandoned
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US8911447B2 (en) | 2008-07-24 | 2014-12-16 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9931059B2 (en) | 2008-09-10 | 2018-04-03 | OrthAlign, Inc. | Hip surgery systems and methods |
US8974468B2 (en) | 2008-09-10 | 2015-03-10 | OrthAlign, Inc. | Hip surgery systems and methods |
US10321852B2 (en) | 2008-09-10 | 2019-06-18 | OrthAlign, Inc. | Hip surgery systems and methods |
US9271756B2 (en) | 2009-07-24 | 2016-03-01 | OrthAlign, Inc. | Systems and methods for joint replacement |
US10238510B2 (en) | 2009-07-24 | 2019-03-26 | OrthAlign, Inc. | Systems and methods for joint replacement |
US9339226B2 (en) | 2010-01-21 | 2016-05-17 | OrthAlign, Inc. | Systems and methods for joint replacement |
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Also Published As
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WO2006058633A1 (en) | 2006-06-08 |
DE102004057933A1 (en) | 2006-06-08 |
ATE554366T1 (en) | 2012-05-15 |
US20070287911A1 (en) | 2007-12-13 |
EP1817547A1 (en) | 2007-08-15 |
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